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The problem of reliable communication over the multiple-access channel (MAC)with states is investigated. We propose a new coding scheme for this problemwhich uses quasi-group codes (QGC). We derive a new computable single-lettercharacterization of the achievable rate region. As an example, we investigatethe problem of doubly-dirty MAC with modulo-$4$ addition. It is shown that thesum-rate $R_1+R_2=1$ bits per channel use is achievable using the new scheme.Whereas, the natural extension of the Gel'fand-Pinsker scheme, sum-ratesgreater than $0.32$ are not achievable.

A New Achievable Rate Region for Multiple-Access Channel with States